An introduction to Gödel's theorems
 Author/Creator
 Smith, Peter, 1935
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2013.
 Physical description
 xvi, 388 p. : ill. ; 25 cm.
 Series
 Cambridge introductions to philosophy.
Access
Available online

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Unknown
QA9.65 .S65 2013

Unknown
QA9.65 .S65 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 372382) and index.
 Contents

 Preface 1. What Godel's theorems say 2. Functions and enumerations 3. Effective computability 4. Effectively axiomatized theories 5. Capturing numerical properties 6. The truths of arithmetic 7. Sufficiently strong arithmetics 8. Interlude: taking stock 9. Induction 10. Two formalized arithmetics 11. What Q can prove 12. I o, an arithmetic with induction 13. Firstorder Peano arithmetic 14. Primitive recursive functions 15. LA can express every p.r. function 16. Capturing functions 17. Q is p.r. adequate 18. Interlude: a very little about Principia 19. The arithmetization of syntax 20. Arithmetization in more detail 21. PA is incomplete 22. Godel's First Theorem 23. Interlude: about the First Theorem 24. The Diagonalization Lemma 25. Rosser's proof 26. Broadening the scope 27. Tarski's Theorem 28. Speedup 29. Secondorder arithmetics 30. Interlude: incompleteness and Isaacson's thesis 31. Godel's Second Theorem for PA 32. On the 'unprovability of consistency' 33. Generalizing the Second Theorem 34. Lob's Theorem and other matters 35. Deriving the derivability conditions 36. 'The best and most general version' 37. Interlude: the Second Theorem, Hilbert, minds and machines 38. muRecursive functions 39. Q is recursively adequate 40. Undecidability and incompleteness 41. Turing machines 42. Turing machines and recursiveness 43. Halting and incompleteness 44. The ChurchTuring thesis 45. Proving the thesis? 46. Looking back.
 (source: Nielsen Book Data)
 Publisher's Summary
 In 1931, the young Kurt Godel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Godel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book  extensively rewritten for its second edition  will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Peter Smith.
 Series
 Cambridge introductions to philosophy
 Note
 Previous ed.: 2007.
 ISBN
 9781107606753
 9781107022843
 1107022843
 1107606756